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FITS World Coordinate Systems



The FITS "World Coordinate System" (WCS) standard defines keywords and usage that provide for the description of astronomical coordinate systems in a FITS image header.

Electronic versions of the four (WCS) papers and related background material are available:

I: "Representations of world coordinates in FITS", Greisen, E.W. & Calabretta, M.R. (2002), Astronomy & Astrophysics, 395, 1061-1075.  

Also a supplement to Paper I entitled Concatenation of FITS World Coordinate Systems by Steve Allen and Doug Mink.

II: "Representations of celestial coordinates in FITS", Calabretta, M.R., & Greisen, E.W., (2002), Astronomy & Astrophysics, 395, 1077-1122.  

III: "Representations of spectral coordinates in FITS", Greisen, E.W., Calabretta, M.R. Valdes, F.G., & Allen, S.L., (2006), Astronomy & Astrophysics, 446, 747-771.  

IV: "Representations of distortions in FITS world coordinate systems", Calabretta et al., draft dated 2004/04/22.

Miscellaneous notes on the derivation of some formulae and special conditions in Paper II, dated 2004/02/11.  

Errata dated 2013/09/21 for Papers I, II & III.

Introduction to celestial coordinate systems; slides (in HTML) from a talk explaining FITS world coordinate systems.


This diagram illustrating Bonne's projection with conformal latitude +35° was produced by WCSLIB, a C implementation of the coordinate transformations defined in the FITS WCS papers. The non-oblique native graticule is in dark green.

The oblique 15° celestial graticule centred on celestial coordinates (0°, +45°) with north celestial pole at native coordinates (45°, 0°) is colour-coded blue, red and white (in increasing order) with the equator and prime meridian in yellow.

"Mapping on the HEALPix grid", Calabretta & Roukema (2007), as accepted by Monthly Notices of the Royal Astronomical Society (MNRAS) on 2007/07/25, describes the HEALPix projection and introduces the HPX projection type in FITS.

The official refereed version of the paper was published as MNRAS 381 865, and can be accessed from ADS .

"Representing the 'Butterfly' Projection in FITS — Projection Code XPH", Calabretta & Lowe (2013), as published with open access in Publications of the Astronomical Society of Australia (PASA) (copyright Cambridge University Press).


Software &c.

WCSLIB is implemented in C, with support for FORTRAN via a set of wrapper functions. A doxygen-generated programming manual (HTML and PDF) is provided.

NEW! (2015/06/29) WCSLIB 5.7 continues the ongoing implementation of WCS distortion functions. While not quite feature-complete, WCSLIB 5.7 implements the framework of WCS Paper IV, together with the general Polynomial distortion defined therein, and a new Template Polynomial Distortion (TPD).

TPD is a superset of the conventional TPV "projection", and the SIP image distortion, which are both fully supported as instances of it.

WCSLIB 5.7 also includes a variety of other improvements.

A general curvilinear axis drawing routine, PGSBOX, for PGPLOT that can optionally interface to WCSLIB, is also included with WCSLIB.

Utility program HPXcvt is included with WCSLIB. It converts 1D HEALPix pixelization data stored in a variety of forms in FITS, including ring or nested organization in a binary table extension, into a 2D primary image array with HPX or XPH coordinate representation.

An example (13MiB bzip'd) is provided of its application to the WMAP 3-year Internal Linear Combination map.

Example FITS files produced for each of the projections in Paper II and for a selection of spectral representations from Paper III, are available for testing purposes.


Dr. Mark R. Calabretta ( mcalabre@atnf.csiro.au)
Last modified: 2015/06/29